A Class of Smoothers for Saddle Point Problems

In this paper smoothing properties are shown for a class of iterative methods for saddle point problems with smoothing rates of the order 1/m, where m is the number of smoothing steps. This generalizes recent results by Braess and Sarazin, who could prove this rates for methods where, in the context of the Stokes problem, the pressure correction equation is solved exactly, which is not needed here. Received December 4, 1998; revised April 14, 2000